Binary Switching Linear Model Control for Lti Systems: Stability Analysis and Mode Control Equivalence

This paper proposes a novel control framework, termed Binary Switching Linear Model Control (BSLMC), for regulating the motion modes of Linear Time-Invariant (LTI) systems. The approach leverages a modal coordinate transformation to decompose an LTI system into a set of decoupled first- and second-order subsystems, enabling selective control of dominant modes without altering the system’s eigenvector structure. By adjusting the natural frequencies and damping ratios of these active modes, the proposed method achieves effective pole reassignment while preserving mode shapes. A frequency-domain analysis demonstrates that the Bode diagram of the original system can be approximated within specific frequency bands by controlling only a subset of modes, thereby reducing computational complexity. Theoretical investigations rigorously analyze the stability of BSLMC using the Lyapunov stability theorem. It is shown that when the switching models form a set of commuting matrices, a common Lyapunov function exists, allowing for arbitrarily small mode-dependent dwell times. For non - commuting cases, a perturbation-based analysis provides conditions for robust stability. The proposed method’s efficacy is validated through numerical simulations on a multi-degree-of-freedom structural system, highlighting its potential for active vibration control and structural dynamics applications.